If you do something illegal because someone asked you to do it, it's still illegal.
Back to your point though, it is a new domain because with your paper examples there is no one who can "undo" the illegal ad. You copy it at Kinko's and it's not like Kinko's is out there delivering it with you. With online platforms, they both Target and deliver these ads and are responsible for continually delivering them.
Example: I worked at a pharmacy with the self-serve digital photo services. A customer brought in a CD and made christmas cards from a family picture.
It turns out the picture was taken by a local photographer the customer had hired. The pharmacy I worked at got the legal notice. Supposedly, we were partly to blame since we profited off of the cards the customer printed. Nevermind the fact that we didn't generally check the customer's pictures, nor could we actually have guessed these were professional vs a good picture.
The customer cropped out the identifying marks. We had all seen pictures that looked professional, both in digital and film form. It seems none of that mattered. It wouldn't be Kinko's fault that you photocopy an illegal ad, but they can be party to the fault by allowing it to be sold.
Now, the USPS probably has completely different laws protecting it. I'm going to guess it is more likely that they try to get you for mail fraud rather than actually hold the USPS responsible.
...Why does a pharmacy print photographies? I've never heard of a pharmacy selling something that isn't drugs.
If you ask USPS to display your illegal ad in their window then it certainly is their fault. That would be an actually comparable situation here.